Approximate solution of the whispering gallery modes and estimation of the spontaneous emission coupling factors for microdisk lasers

Abstract

The threshold current of a microcavity laser with low transparency current is dependent mainly on the spontaneous emission coupling factor, β, which is the spontaneous emission rate into the lasing mode divided by the total spontaneous emission rate. The spontaneous decay may be modeled as stimulated decay due to stochastic vacuum field fluctuations.1 The decay rate, γ, of a dipole due to a mode (either radiation mode or guided mode) depends on the spatial mode area and the modal density of states.1 To estimate the β value for a microdisk laser2 where exact solutions are difficult to obtain, a simple approximate method for solving the waveguide modes and the density of states is developed here.